The station has since reopened and police in Paris have confirmed to CNN that the security alert was a false alarm.

Around the world

Outside of Belgium, security has tightened at European airports and U.S. cities have also ramped up security.

The British government has warned its citizens to be vigilant when visiting Belgium, which has now been placed at threat level 3 -- meaning "a possible and real threat."

"You should remain alert and vigilant, especially in places where there's a high concentration of people," said the UK Home Office.

"Belgian security operations are likely to be carried out at short notice. If you're in an affected area you should follow the instructions of the Belgian security authorities. Police have asked the public not to comment on police operations on social media," it added.

Similarly, the Australian government has urged citizens to use a "high degree of caution" when traveling to Brussels.

"Travelers are reminded that there is a heightened potential for police raids to take place with little or no warning in response to the raised terrorism threat," it said.

Lufthansa, Air France, KLM, British Airways, American Airlines, United Airlines, Delta Airlines, Ryanair, Alitalia and Easyjet have all canceled or diverted flights.

Aegean is offering free rebookings or full refunds to any passengers who want to cancel their Brussels flights between now and March 31.

Aer Lingus is offering free changes or refunds to customers traveling on affected Brussels flightson March 22 and 23.